Marcel flew 6090 miles from New York to Japan for Christmas. For Valentine's Day marcel flew from New York to England.The distance from New York to England's is 2/3 of the distance from New York to japan. How many miles did marcel fly for Valentine's Day?

Answer:

It would take skinny cat 6 mins to reach fat cat.

Step-by-step explanation:

Given:

Speed of Fat cat = 75 yd/min

Speed of skinny cat = 100 yd/min

We need to find the time taken by skinny cat to reach fat cat.

Let the distance covered by both be 'd'.

Also let the time taken by Fat cat to cover distance 'd'  be 't' mins.

Now we know that skinny cat started 2 mins later so time taken by Skinny cat will be [tex]t-2 \ mins[/tex].

Now we know that;

Distance is equal to speed times time.

framing in equation form we get;

Distance cover by fat cat = [tex]75t[/tex]

Distance cover by skinny cat = [tex]100(t-2) =100t-200[/tex]

Both distance have to made same since we need to find the time required more to reach the other cat.

[tex]100t-200=75t[/tex]

Combining like terms we get;

[tex]100t-75t=200\\\\25t =200[/tex]

Dividing both side by 25 we get;

[tex]\frac{25t}{25}=\frac{200}{25}\\\\t = 8\ mins[/tex]

Time taken by skinny cat = [tex]t-2 =8-2=6 \ mins[/tex]

Hence it would take skinny cat 6 mins to reach fat cat.

Skinny Cat catches up to Fat Cat 6 minutes after starting at 9:02 am, which is at 9:08 am. This is calculated by determining the head start that Fat Cat has and the faster pace at which Skinny Cat moves.

We are presented with a problem where two cats, one named Fat Cat and the other Skinny Cat, start at different times and move at different speeds. Fat Cat starts at 9:00 am moving at 75 yards per minute, and Skinny Cat starts at 9:02 am moving at 100 yards per minute. The question is to find out how long it takes for Skinny Cat to catch up to Fat Cat.

So, Skinny Cat will catch up to Fat Cat 6 minutes after starting at 9:02 am, which is at 9:08 am.

Answer:

Step-by-step explanation:

In our triangle, angles E + F + G = 180 degrees.  If angle E is 4 times the measure of F, and G is 18 less than E, then

F is x,

E is 4x, and

G is 4x - 18

Add these all together and set the sum equal to 180:

x + 4x + 4x - 18 = 180

Combining like terms:

9x - 18 = 180 and

9x = 196 so

x = 22

That means that

F = 22,

E = 4(22) = 88 and

G = 4(22) - 18 = 88 - 18 = 70

Since 22 + 88 + 70 do in fact equal 180 you can be fairly certain that your answer is correct! (It is correct...trust me!)

Answer:

50.75 units

Step-by-step explanation:

In this problem

Triangles HFM and PST are similar

we know that that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

step 1

Find the scale factor

Let

z ----> the scale factor

[tex]z=\frac{HF}{PS}[/tex]

substitute the given values

[tex]z=\frac{14}{8}=1.75[/tex]

step 2

Find the perimeter of triangle PST

[tex]P=8+9+12=29\ units[/tex]

step 3

Find the perimeter of triangle HFM

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

The perimeter of triangle HFM is equal to the perimeter of triangle PST multiplied by the scale factor

so

[tex]29(1.75)=50.75\ units[/tex]

Stem and Leaf plot would be the best choice to display the given data if we want to display the numbers which are outliers as well as the mean.

Hence option C is correct.

Given, representation of outliers and mean.

Data: [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32]

Stem and Leaf plot would be the best choice to display the given data if we want to display the numbers which are outliers as well as the mean.

Therefore option C is correct.

Know more about stem and leaf plot,

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Options for question :

1) Pie Graph

2) Bar Graph

3) Stem and Leaf Plot

4) Line Chart

5) Venn Diagram

A box and whisker plot is the best choice to display data including outliers and the mean in mathematics. It clearly shows the median, quartiles, and outliers. The mean can be depicted as an additional point.

In the field of mathematics, to display the data with outliers and the mean, a box and whisker plot is the most suitable graph. This type of graph can highlight outliers and also show the mean. For instance, our given data [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32] when plotted on a box and whisker plot would display the median (the line inside the box), the quartiles (the ends of the box), and outliers (points outside the whiskers). The mean can additionally be added as a separate point on the plot.

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ANSWER: Adult tickets: 200  Student tickets:400

STEP-BY-STEP EXPLANATION:

n = number of adult tickets sold

2n = number of student tickets sold

2n(1.25) + n(1.75) = $850

2.50n + 1.75n = $850

4.25n = $850

n = 200

2n= 2 × 200= 400

Answer:888 cubic centimeters

Step-by-step explanation:

The formula for determining the volume of a rectangular prism is expressed as

Volume = length × height × width

Length = 10 centimeters

Width = 8 centimeters

Height = 12 centimeters

Therefore, the volume of the rectangular prism would be

10 × 8 × 12 = 960 centimeters³

A rectangular hole with a length of 2 centimeters and a width of 3 centimeters is cut through the prism. The height of the hole would also be 12 centimeters.

Therefore, the volume of the rectangular hole would be

2 × 3 ×12 = 72 cm³

the volume of the resulting figure would be

960 - 72 = 888 cm³

Answer:

The answer to your question is below

Step-by-step explanation:

Data

P (-5, 5)

Parallel to 6x - 5y - 9 = 0

Process

1.- Find the equation of the line

                  6x - 5y = 9

                       -5y = -6x + 9

                          y = -6/-5 x + 9/-5

                          y = 6/5 x - 9/5

slope = 6/5, as the lines are parallels, the slope is the same.

2.- Get the equation of the new line

                     y - y1 = m(x - x1)

                     y - 5 = 6/5 (x + 5)

                     y - 5 = 6/5x + 6

                          y = 6/5x + 6 + 5

                          y = 6/5x + 11                     Point-slope form

                   5y - 25 = 6(x + 5)

                   5y - 25 = 6x + 30

                   6x - 5y + 30 + 25 = 0

                  6x - 5y + 55 = 0                      General form

The equation of the line that passes through (-5,5) and is parallel to 6x - 5y - 9 = 0 can be written in point-slope form as y - 5 = (6/5)(x + 5) and in general form as -6x + 5y - 55 = 0.

To write an equation for the line that passes through the point (-5,5) and is parallel to the line 6x - 5y - 9 = 0, we first need to find the slope of the given line. By rewriting the equation in slope-intercept form (y = mx + b), we can identify the slope (m). The equation 6x - 5y - 9 = 0 can be rewritten as y = (6/5)x + 9/5, so the slope of the line is 6/5. Since parallel lines have the same slope, the slope of our new line is also 6/5.

Next, we use the point-slope form of the equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line (here (-5,5)) and m is the slope. Substituting these values into the equation gives us y - 5 = (6/5)(x + 5).

To express this in general form (Ax + By + C = 0), we rearrange the equation: multiply both sides by 5 to clear the fraction, resulting in 5(y - 5) = 6(x + 5), which simplifies to 5y - 25 = 6x + 30. Rearranging gives -6x + 5y - 55 = 0.

Answer:

Siham ran for 305 minutes

Step-by-step explanation:

Let

Siham Ran for time = X

Siham Ran for time = X-60

According to given condition

X + (X-60) = 670

X + X - 60 = 670

2X = 670-60

2X = 610

X = 610/2

X = 305

So Siham ran for 305 minutes only

Answer:

Byte

Step-by-step explanation:

We use byte to represent 1 and 0 in computing..

The most basic unit of computing is the 'bit', which can be represented as either 1 (on) or 0 (off). This binary information is used in digital circuits to perform tasks in computing devices. The use of bits was crucial to the development of modern computing.

The most fundamental unit of computing is the bit, which is represented as an on (1) or off (0) value. In digital circuits found in modern devices, transistors behave like switches that can be either on or off, encoding information in a binary code of ones and zeros. These bits are utilised to perform a variety of tasks like data manipulation and transmission of signals. Over time, scientists have found ways to amplify the computing capacity of bits by integrating vast collections of transistors on single silicon wafers, creating the integrated circuits (IC), which is foundational to the modern digital computer revolution.

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Answer:he borrowed $22000 from bank 1.

He borrowed $2000 from bank 2

Step-by-step explanation:

Let x represent the amount of money that he borrowed from bank 1.

Let y represent the amount of money that he borrowed from bank 2.

Bobby Borrowed 24,000 from two different banks to start a business. This means that

x + y = 24000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time

Considering the money borrowed from bank 1,

P = x

R = 4%

T = 1

I = (x × 4 × 1)/100 = 0.04x

Considering the money borrowed from bank 2,

P = y

R = 5.5%

T = 1

I = (y × 5.5 × 1)/100 = 0.055y

if the total interest after 1 year was $990, it means that

0.04x + 0.055y = 990 - - - - - -1

Substituting x = 24000 - y into equation 1, it becomes

0.04(24000 - y) + 0.055y = 990

960 - 0.04y + 0.055y = 990

- 0.04y + 0.055y = 990 - 960

0.015y = 30

y = 30/0.015 = $2000

Substituting y = 2000 into

x = 24000 - y, it becomes

x = 24000 - 2000

x = 22000

Answer:

Step-by-step explanation:

Let x represent the number of farmers that grew all three crops.

Let y represent the number of farmers that grew corn and oat.

The Venn diagram representing the scenario is shown in the attached photo.

W represents the subset for wheat

C represents the subset for corn

O represents the subset for oat

199 grew wheat. It means that

121 + 57 - x + x + 60 - x = 199

238 - x = 199

x = 238 - 199

x = 39

182 grew corn. It means that

113 + 60 - x + x + y - x = 182

173 + y - x = 182

y = 182 - 173 + 39

y = 48

a) the number of farmers who grew at least one of the three would be

121 + 113 + 90 + 57 - x + 48 - x + 60 - x + x

= 121 + 113 + 90 + 57 - 39 + 48 - 39 + 60 - 39 + 39 = 411

b) the number of farmers that grew all three would be

x = 39

c) the number of farmers who did not grow any of the three would be

500 - 411 = 89

d) the number of farmers who grew exactly two of the three would be

60 - x + 57 - x + 48 - x

= 60 - 39 + 57 - 39 + 48 - 39

= 21 + 18 + 9

= 48

The number of farmers who grew at least one of the crops is 328, all three is not stated, none of the three is 172 and exactly two of them is 117.

To solve this problem, we have to understand Venn Diagrams and set theory. When adding up counts for different categories, it is important to not double count any item.

The number of farmers who grew at least one of three crops (wheat, corn, oats) can be determined by the sum of all the individual and intersection categories. However, we subtract the counts that have been mentioned twice.

a) At least one: (121 wheat only + 113 corn only + 90 oats only + 199 wheat + 60 wheat&corn + 57 wheat&oats + 182 corn) - (2*(60 wheat&corn) + 2*(57 wheat&oats) + 2*(182 corn&-)) = 328

b) All three: There is no clear information about farmers growing all three crops. We may assume it to be 0, as it is not stated.

c) None of three: The survey includes 500 farmers, if 328 grow at least one crop, then the number of farmers that did not grow any of the three is 500 - 328 = 172

d) Exactly two: 60 grew wheat and corn, 57 grew wheat and oats. Hence 117 farmers grew exactly two of the three crops.

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Answer:B

Step-by-step explanation:

Given

Right circular cone is inscribed in a hemisphere so that the base of the cone coincides with base of hemisphere

Height of cone is equal to radius of hemisphere

so ratio of the height of cone to the radius of the hemisphere is 1:1

STEP-BY-STEP EXPLANATION:

Let be x the number of boxeds of crackers you can buy

If each box has a cost of $2.30 and you have $11.50

we can represent this into this equation

2.30x= 11.50

x=[tex]\frac{11.50}{2.30}[/tex]

x=5

You can buy 5 boxes of crackers

Answer:

89.04% of the data points will fall in the given range of z = − 1.6 and z = 1.6      

Step-by-step explanation:

We are given a normally distributed data.

We have to find the percentage of data that lies within the range  z = − 1.6 and z= 1.6

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

[tex]P(-1.6 \leq z \leq 1.6)\\= P(z \leq 1.6) - P(z \leq -1.6)\\\text{Calculating the value from standard normal table}\\= 0.9452 - 0.0548 = 0.8904= 89.04\%[/tex]

89.04% of the data points will fall in the given range of z = − 1.6 and z= 1.6

Final answer:

Approximately 89.04% of data points fall within 1.6 standard deviations of the mean in a normally distributed set, calculated using the empirical rule and Z-table for the standard normal distribution.

Explanation:

To find the percentage of data points that fall between z-scores of -1.6 and 1.6, we use the properties of the standard normal distribution. Based on the empirical rule (also known as the 68-95-99.7 rule), we know that approximately 68% of data points lie within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean in a normal distribution.

Since our z-scores are between -1 and 2, we will look at the percentages for these intervals. Typically, a z-score of 1.6 would correspond to a value between the percentages for 1 and 2 standard deviations from the mean. Using a Z-table or standard normal distribution curve calculator, we find that a z-score of 1.6 gives us approximately 0.4452 (or 44.52%) to the left of the z-score and 0.4452 to the right. Therefore, the total area between -1.6 and 1.6 is 2 × 0.4452, which is approximately 0.8904 (or 89.04%). Thus, approximately 89.04% of the data points will fall within 1.6 standard deviations from the mean in a normally distributed data set.

Answer:

40.112

Step-by-step explanation:

Answer:

C. The term linear refers to a straight line, and r measures how well a scatter plot fits a straight-line pattern

Step-by-step explanation:

In statistics, when two variables are being investigated, the location of the co-ordinates on a rectangular co-ordinates ystem is called a scatter diagram.

The amount of linear correlation between two variables is expressed by a coefficient of correlation, given the symbol r. This is defined in terms of the deviations of the co-ordinates of two variables from their mean values and is given by the product-moment formula

For linear correlation, if points are plotted on a graph and all the points lie on a straight line, then perfect linear correlation is said to exist. When a straight line having a positive gradient can reasonably be drawn through points on a graph positive or direct linear correlation exists.

Answer:

See the plot below.

For this case we can consider as an outlier the value 8.0 since is far away from the other points

Step-by-step explanation:

For this case we can create the stem plot like this:

Stem      Leaf

 0      |     5 7

 1       |     1 2 2 3 3 5 5 7 7 8 9

 2      |     0 2 5 6 8 8 8

 3      |     5 8

 4      |     4 8 9

 5      |     2 5 7 8

 6      |

 7      |

 8      |    0

Notation : "1 |1 means 1.1 for example and 3|5 means 3.5"

By definition an outlier is "an observation that lies an abnormal distance from other values in a random sample from a population"

For this case we can consider as an outlier the value 8.0 since is far away from the other points

Answer:

The sampling used is simple random sampling.

Step-by-step explanation:

Consider the provided information.

Types:

Here, randomly selected 60 customers, Thus, the sampling used is simple random sampling.

Answer:

a) The problem says that this represent the values within 3 deviations from the mean and using the empirical rule we know that on this case we have 68% of the data on this interval.

b) For this case we can use the z score formula again:

[tex] z_1= \frac{98.73-98.38}{0.48}=0.729[/tex]

[tex] z_2= \frac{97.89-98.38}{0.48}=-1.020[/tex]

For this case we want this probability:

[tex] P(97.89<X<98.73) =P(-1.02<Z<0.729)= P(Z<0.729)-P(Z<-1.02)=0.767-0.154= 0.613[/tex]

So the approximate percentage of temperatures between 97.89F and 98.73F is 61.3%

Step-by-step explanation:

The empirical rule, also referred to as "the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)". The empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

For this case we know that the body temperatures for a group of heatlhy adults represented with the random variable X follows this distribution:

[tex] X \sim N(\mu =98.38F, \sigma=0.48 F)[/tex]

Part a

For this case we can use the z score formula to measure how many deviations we are within the mean, given by:

[tex] z=\frac{x-\mu}{\sigma}[/tex]

If we find the z score for the values given we got:

[tex] z_1= \frac{99.57-98.38}{0.48}=2.479[/tex]

[tex] z_2= \frac{97.05-98.38}{0.48}=-2.771[/tex]

The problem says that this represent the values within 3 deviations from the mean and using the empirical rule we know that on this case we have 68% of the data on this interval.

Part b

For this case we can use the z score formula again:

[tex] z_1= \frac{98.73-98.38}{0.48}=0.729[/tex]

[tex] z_2= \frac{97.89-98.38}{0.48}=-1.020[/tex]

For this case we want this probability:

[tex] P(97.89<X<98.73) =P(-1.02<Z<0.729)= P(Z<0.729)-P(Z<-1.02)=0.767-0.154= 0.613[/tex]

So the approximate percentage of temperatures between 97.89F and 98.73F is 61.3%

The reciprocal of n must be less than –10

Solution:

Given n denotes a number to the left of 0 means n < 0.

Square of n is less than [tex]\frac{1}{100}[/tex] means [tex]n^2<\frac{1}{100}[/tex].

Therefore, we have [tex]n<0[/tex] and [tex]n^2<\frac{1}{100}[/tex].

⇒ [tex]n^2<\frac{1}{100}[/tex]

Taking square root on both sides, we get

⇒ [tex]n<\± \frac{1}{10}[/tex]

⇒[tex]\frac{-1}{10}<n<\frac{1}{10}[/tex]

⇒ But we know that n < 0, so [tex]n<\frac{1}{10}[/tex] false.

It should be [tex]\frac{-1}{10}<n[/tex].

To equal the expression, multiply both sides of the equation by –10n.

⇒ [tex]-\frac{1}{10} \times\frac{-10}{n}>n \times\frac{-10}{n}[/tex]   (symbol < changed to > when multiply by minus)

⇒ [tex]\frac{1}{n}>-10[/tex]

Hence, the reciprocal of n must be less than –10.

Answer:

XY is 4 units.              

Step-by-step explanation:

We are given the following in the question:

Right triangle ABC is similar to triangle XYZ.

AB = 20.8 units

BC = 36.4 units

YZ = 7 units

We have to find the length of side XY.

Since the given triangles are similar, they have the following property:

The ratio of corresponding sides of similar triangles are equal.

We can write,

[tex]\displaystyle\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex]

Putting the given values, we have,

[tex]\displaystyle\frac{AB}{XY}=\frac{BC}{YZ}\\\\\frac{20.8}{XY}=\frac{36.4}{7}\\\\XY = \frac{20.8\times 7}{36.4} =4 \text{ units}[/tex]

Thus, the length of XY is 4 units.

Answer:

The number is 226.

Step-by-step explanation:

Let the number be x.

Given:

The number is greater than two hundred twenty-five.

So we can say that;

[tex]x>225[/tex] equation 1

Also Given:

Her number is less than 2 hundreds,2 tens, and 7 ones.

Now we can say that 2 hundreds,2 tens, and 7 ones is equal to 227

So now the number is less than 227.

[tex]x<227[/tex] equation 2

From equation 1 and equation 2 we can say that;

[tex]225<x<227[/tex] equation 3

Also,

[tex]225<226<227[/tex] equation 4

Comparing equation 3 and 4 we get;

[tex]x=226[/tex]

Hence The number is 226.

Answer: [tex]137\dfrac{1}{3}\ cm,\ 137\dfrac{1}{3}\ cm,\ 250\dfrac{1}{3}\ cm[/tex]

Step-by-step explanation:

Let x be the equal sides of the triangle .

The , the third side would be x+113 cm.

The perimeter is the sum of all sides of a triangle.

So , The perimeter of triangle would be  x+x+(x+113)= 3x+113 --------(1)

Since , it is given that the perimeter of triangle is 525. -----(2)

So from (1) and (2) , we have

[tex]3x+113=525\\\\ 3x=525-113=412\\\\ x=\dfrac{412}{3}=137\dfrac{1}{3}[/tex]

Then, third side = [tex]137\dfrac{1}{3}+113=250\dfrac{1}{3}\ cm[/tex]

Hence , the sides of a triangle  are:[tex]137\dfrac{1}{3}\ cm,\ 137\dfrac{1}{3}\ cm,\ 250\dfrac{1}{3}\ cm[/tex]

Answer: 1 16/45, 1 16/45, 2 31/45

Step-by-step explanation:

Say x is the equal side of the triangle.

The third side would be x+113 cm.

The perimeter is the sum of all sides of a triangle.

So, the perimeter of the triangle would be  x+x+(x+113)= 3x+113

Since the triangle's perimeter is 5 2/5, 3x + 1 1/3 = 5 2/5.

1 1/3 is 1 5/15. 5 2/5 is 5 6/15. 5 6/15 - 1 5/15 = 4 1/15.

This means 3x = 4 1/15.

4 1/15 = 61/15

3x = 61/15

To make 3x into x, you can multiply it by 1/3.

3x*1/3 is x. 61/15*1/3 = 61/45.

x = 1 16/45 because 61/45 = 1 16/45.

The longer side is x + 1 1/3 so you have to add 1 1/3 to 1 16/45 which is

2 31/45.

So, the sides are 1 16/45, 1 16/45 and 2 31,45.

9514 1404 393

Answer:

  each has to work 5 hours and earn $42

Step-by-step explanation:

Let m and h represent hours Nai spends mowing and hauling, respectively. Then (m+h) will be the number of hours Priya spends babysitting. In order for their earnings to be equal, we must have ...

  7m +14h = 8.40(m+h)

  5.60h = 1.40m . . . . . . . . subtract 7m+8.40h

  m = 4h . . . . . . . . . . . . . . divide by 1.40

Then the total number of hours worked by either person is ...

  m + h = (4h) +h = 5h

If only whole numbers of hours are worked, then the smallest number of hours that will make earnings equal is 5h, with h=1, or 5 hours. In that time, each will earn 5×$8.40 = $42.

Each must work 5 hours and earn $42 before they go to the movies.

__

Nai will work 4 hours mowing and 1 hour hauling.

Priya and Nai have to work 0 hours before they go to the movies.

To find out how much money Priya and Nai each have to work before they go to the movies, we need to set up an equation. Let x represent the number of work hours for both Priya and Nai. Nai earns $7 per hour, so her earnings in x hours would be 7x dollars. Priya earns $8.40 per hour, so her earnings in x hours would be 8.40x dollars. Since they want to earn the same amount, we can set up the equation:

7x = 8.40x

To solve for x, we can subtract 7x from both sides of the equation:

0.40x = 0

Now, divide both sides of the equation by 0.40 to solve for x:

x = 0 / 0.40

x = 0

Therefore, both Priya and Nai have to work 0 hours before they go to the movies. This means they have already earned the same amount of money.

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Answer:

DIRECT WAY EXCEL

"=NORM.DIST(75,80,3,TRUE)"

And we got: [tex] P(X\leq 75)= 0.04779[/tex]

OTHER WAY

[tex]P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z<-1.67)[/tex]

And we can find this probability using the normal standard table or excel:

[tex]P(Z<-1.67)=0.04779[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the diameter of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(80,3)[/tex]  

Where [tex]\mu=80[/tex] and [tex]\sigma=3[/tex]

And we know that if the diameter is 75 or less the ring would be considered defective , so then in order to find the proportion of defective we need to find the following probability:

[tex] P(X\leq 75)[/tex]

One way to do this in excel is with the following formula:

"=NORM.DIST(75,80,3,TRUE)"

And we got: [tex] P(X\leq 75)= 0.04779[/tex]

And the other way is use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z<-1.67)[/tex]

And we can find this probability using the normal standard table or excel:

[tex]P(Z<-1.67)=0.04779[/tex]

Answer:

The regular price of the car is $13,000.

Step-by-step explanation:

i) let the price of the van Andy and Diane want to buy be $x.

ii) they get $5,500 for their present car

iii) they also make a down payment of $2,300.

iv) therefore $x = $0.4x + $5,500 +  $2,300

   therefore $0.6x = $7,800

therefore $x = $[tex]\frac{7800}{0.6}[/tex] = $13,000

The regular price of the car is $13,000.

Answer:

The average life of the mice that are placed on this diet is less than 40 months.

Step-by-step explanation:

Consider the provided information.

When 40% of the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ < 40.

The null and alternative hypothesis are:

[tex]H_0:\mu=40\\H_a:\mu<40[/tex]

64 mice that are placed on this diet have an average life is 38 months with a standard deviation of 5.8 months.

Therefore, [tex]n = 64, \bar x=38\ and\ \sigma=5.8[/tex]

Use the formula: [tex]z=\dfrac{\bar x-\mu}{\frac{\sigma}{\sqrt{n} }}[/tex]

Substitute the respective values in the above formula.

[tex]z=\dfrac{38-40}{\frac{5.8}{\sqrt{64} }}[/tex]

[tex]z=-\dfrac{2}{\frac{5.8}{8}}\approx-2.76[/tex]

Now using the table [tex]P(Z<z)=0.029[/tex]

The p value is smaller than 0.05 so reject the null hypothesis.

Therefore, the average life of the mice that are placed on this diet is less than 40 months.

Answer:

(0.2599,0.3401)                                                

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 500

x = 150

[tex]\hat{p} = \dfrac{x}{n} = \dfrac{150}{500} = 0.3[/tex]

Confidence interval:

[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96[/tex]

Putting the values, we get:

[tex]0.3\pm 1.96\sqrt{\dfrac{0.3(1-0.3)}{500}} = 0.3 \pm 0.0401 =(0.2599,0.3401)[/tex]

The 95% confidence interval is (0.2599,0.3401).

Answer:

[tex]x^{4}[/tex] + 3x² - 4

Step-by-step explanation:

Note that complex zeros occur in conjugate pairs

If 2i is a zero then - 2i is a zero

The zeros are x = 1, x = - 1, x = 2i, x = - 2i, thus the factors are

(x - 1), (x + 1), (x - 2i) and (x + 2i)

The polynomial is expressed as the product of the factors, thus

f(x) = (x - 1)(x + 1)(x - 2i)(x + 2i) ← expanding in pairs

     = (x² - 1)(x² - 4i²) → i² = - 1

     = (x² - 1)(x² + 4) ← distribute

     = [tex]x^{4}[/tex] + 4x² - x² - 4

     = [tex]x^{4}[/tex] + 3x² - 4